dsl/compiler: Fix&tidy PETSc mixed solver functionality #8071

Job	Run time
pytest-ubuntu-py311-gcc11-cxxnoomp-adjoint	37m 19s
pytest-ubuntu-py39-gcc14-omp-adjoint	37m 45s
pytest-ubuntu-py312-gcc12-cxxomp-base	1h 3m 47s
pytest-ubuntu-py39-gcc14-omp-base	50m 10s
pytest-ubuntu-py312-gcc12-cxxomp-adjoint	46m 36s
pytest-ubuntu-py311-gcc11-cxxnoomp-base	50m 47s
pytest-ubuntu-py312-gcc13-omp-base	57m 51s
pytest-ubuntu-py312-gcc13-omp-adjoint	42m 41s
pytest-docker-py39-gcc-omp-base	43m 19s
pytest-docker-py39-icx-omp-base	35m 11s
pytest-ubuntu-py39-gcc9-omp-base	50m 29s
pytest-ubuntu-py310-gcc10-noomp-adjoint	34m 20s
pytest-osx-py312-clang-omp-base	29m 47s
pytest-ubuntu-py310-gcc10-noomp-base	47m 15s
pytest-docker-py39-icx-omp-adjoint	31m 31s
pytest-docker-py39-gcc-omp-adjoint	31m 45s
pytest-ubuntu-py39-gcc9-omp-adjoint	36m 51s
	12h 7m 24s

Provide feedback